Availability and accessible education across all groups and layers of society is undoubtedly a fundamental right. But I only partly agree that all forms of education should be completely funded by governments. In my view, basic and colleague level education should be free and accessible to everyone, while universities should remain the current structure with tuition fees for general public and scholarships for talented people.
I believe primary and secondary education should be guaranteed by governments. It is the basic form of education which is necessary for lifetime learning and transferable knowledge. If access depends only on family income, it would create more inequality between different social groups and many capable students would left behind. Fortunately, most countries share this idea. For example in most of European Union countries schools and professional colleagues are free, which results in statistics of lower poverty rate and higher average income. In addition, I would extend government support for all most needed professions, like nurses, fire fighters, and others. High demand professions should be well funded and accessible to collect necessary amount of workers.
Another topic is universities and postgraduates. I think current model with scholarship for talented people and tuition fees for others is working and proved it stability over the years. Otherwise, it would create an excessive pressure on the public finance and taxpayers. Such an approach, which most countries have at the moment, allows to allocate resources more effectively, while still supporting students who has skills but not funds to pursue their dreams.
To conclude, education should be recognised as necessity for society in order to be in balance and to have less inequality. The more educated people we have the more economical growth we will get. But taxpayers should not cover the entire cost on all levels, otherwise it would burden the public finances.